# Full text of "History Of The Theory Of Numbers - I"

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```SUBJECT INDEX
485
Farey series, 155-8 Fermatian function, 385 Fermat,'s-jaumbers 22°4-l, 94,
140A99>375, 398, 401 ---------^Cneorem, 12, 17, 18,
59-89,179
-, converse of,
91-5
-, generaliza-
tion, 84-9, 406 (see Galois) Finite algebra, 388 --------differences, 250, 394,
407
---------field, 247, 250
Flachen Zahlen, 4 Frequency of a divisor, 126
Galois field, 232, 247, 250
--------imaginary, 233-55   .
Galois' generalization of Fer-mat's theorem, 235, 240, 246-7, 249, 250, 252, 403
---------------------------Wilson's theorem, 240, 246-7, 252
Gaussien, 194
Graphical factoring, 351,353-4, 356, 365, 369, 372, 374
--------representation of divisors, 330, 351, 354
Greatest common divisor, 139, 147, 150, 252, 328, 332-6, 394, 401-3, 447, 456, 462 (see determinant of Smith)
--------divisor, 329, 331
--------integer in, 89, 119,
121-2, 126, 13C, 132, 138, 144, 153, 158, 263, 282, 293, 295, 297-9, 302-3, 319, 427, 429-432, 450-1
Goldbach's theorem and analogues, 421-5
Golden section, 411
Ground forms, 268
Groups, 78, 80-1, 84-5, 131, 137, 152, 155, 177, 194, 196-8, 201, 203, 216, 221, 248, 251, 268, 287, 332, 356, 414-5
Haupt-exponent, 190,200,203
Hexagon, 9, 411
Highest prime power in m.!, 263, 272
nomial, 334
Highly composite number,l323 History,  32,   84,   157,   200,
342, 353 Hyper-even number, 379
Hyper-exponential   number, 379
Idoneal (idoneus), 361-5 Imperfectly amicable, 50 Index, 85, 182-3, 185, 188,
190-4, 197-204, 211, 240,
244-5, 249, 251 Indian, 337 Indicator, 118, 131, 155, 186,
194, 200 Indivisibilis, 6 Integral logarithm, 353, 417,
440
Invariant, 89, 232-3, 260,364 Inversion, 84, 120, 127, 129,
132-3, 135, 140, 145, 150,
153,  234,  296,  429,   430,
441-8
Irreducible function, 234-252 ---------   fraction,   126,   129,
133, 138, 155-8, 162, 175
Kerne, 334 K6rper Zahlen, 4 Kronecker's plane, 155
Lattice, 173
Leaf arrangement, 411
Least common multiple, 82,
328, 332-6, 445, 464
---------residue, 341-2,344,369
Legendre-Jacobi symbol, 109,
210,219,249,251,255,260,
276, 288, 300, 308, 330,364,
382, 385, 394, 398 Linear differential form, 248,
250 ---------forms of divisors, 160,
362-4, 370, 382, 386, 390,
399
-function, 117-8, 134,
204-5
- numbers, 4
Lucas' un, vn, 218, 395, 418 Lucassian, 27
Mangelhaft, 3
Matrix, 137, 226, 228, 233
Maximum divisor, 332
Mean, 281, 291-4, 301-2, 305, 312,318,320,328-331,333, 335, 447 (see asymptotic)
Mediation, 156
Mersenne number, 31
Mobius' (Merten's) function M(n), 86, 122, 127-9, 144-5, 148-9,150-1, 265,289, 322-3, 329, 335, 431, 441-9, 462
----------------------------generalized, 135-3
'Modular   system,   88,   249,
251, 402 Mosaic, 212 Multinomial  coefficient,  59,
266-78 Multiply perfect, 33
Nim (game), 460
Nombres associe"s, 50
Norm, 236, 252, 322
Normal order, 325
Number of divisors, 51, 54, 135-6, 142, 279-325, 328, 443, 451
------------------integers divisible by nth power, 327-32 solutions of
t*i. .. uk=n, 125,149,291, 298, 308, 312, 317, 324
318
Numerical integrals and derivatives, 152, 449
Order modulo m, 138 --------of root, 18.9
Partial fraction, 73, 135, 161,
198, 410 Partition, 279, 290, 292, 303,
312, 427, 438 Patrone, 349
Pedal triangle, 86, 388,402 Pell equation, 56, 367-8, 393 Pentagonal number, 279, 292,
312
Perfect number, 3-33, 38 -----------------of second kind,
58
Period, 133, 182, 202, 207 Periodic fraction,  75-6, 82,
92, 159-179, 193, 202, 339-
341j 371, 379, 386, 454 Permutations, 78-80,131,136 Plateau's theorem, 456, 460,
463
Pluperfect, 33 Plus quam-perf ectus, 3 Polygon, curvilinear, 85 --------, inscribed   in   cubic
curve, 85, 150 --------, regular, 71, 75, 133,
139, 193, 375 Polynomial, divisors of, 384,
393-4 ---------in x divisible by m for
every x, 87, 89, 336 Primary function, 240 Prime functions (see irreducible) ---------pairs, 353, 425, 438```